Is the EMH AI somehow technologically inferior to Soong androids?

Data is an engineering marvel in terms of his body and his brain being beyond state of the art nanotechnology that federation science can't duplicate.

The EMH or Moriarty the original sentient hologram are just brute force consequences of computer power and programming with a mundane holographic interface.

So basically the self awareness that should have made Data special was diminished by in universe technology even in TNG. I'd say the legal and philosophical implications of this were completely ignored. And the answer to your question is that folks who work on AI are really working on nanotechnology that produces AI.

• The holodeck accidentally created a self-aware Moriarty when Geordi asked it to create an opponent that could beat Data.
• Data himself discovered a group of maintenance robots that had accidentally become self-aware on Tyrus VIIa .
• Even the Enterprise's main computer accidentally became self-aware while Data was still on-board.

So, even ignoring the Emergency Medical Hologram*, accidental artificial intelligence (in the sense of artificial consciousness) is apparently a semi-regular occurrence in the Next Generation time frame. (It probably would have happened more during the Original Series if it weren't for Kirk running around shouting the Liar's Paradox at anything that looked a bit like an android.)

Intentional artificial intelligence, however, is apparently more difficult. Data, and his kin, were the only known example of sentient androids being intentionally and successfully designed and created. No-one else — including Data — could figure out how reproduce that achievement.

As per Star Trek: Picard, the Daystrom Institute eventually successfully created synths. This work may have been informed by studies of Voyager's EHM and similar emergent AIs, although the synths didn't quite seem to have the same degree of sentience as Data or the Doctor. Perhaps the emergent AIs were studied, but it wasn't possible to understand or reproduce what led to their emergence**.

STAR TREK: PICARD SPOILERS AHEAD:

_{* A difficult, but necessary task at the best of times.}

_{** Or those pesky Federation ethics limited the amount of study that could be done. I hold out hope that the Doctor wasn't terminated under the AI laws, and serves as a kind of benevolent tenor King on a planet of sentient holograms somewhere. If you know anyone on the Picard season 2 staff, I have a great spec script for them.}

An additional thought stemming from lucasbachmann's answer is that while they are of comparable sentience the EMH requires (at least prior to the mobile emitter attained via time travel, and the federation probably has rules about trying to research items attained from the future) an entire ship's computer, while data is mobile in his own right.

Portability

Most of the AIs seen in Star Trek are housed in starship Main Computers.

The ship's computer AI is (obviously) housed in the Main Computer.
The Holodeck characters that gained spontaneous emergent intelligence (Moriarity, Fairhaven etc) are all constructed by the ship's Main Computer.
Though Moriarity is eventually transferred to a portable device to keep the simulation running indefinitely. The possibility that the simulation is running a lot slower to allow for lesser hardware is unstated, but explains why the holodeck is usually run via the main computer rather than its own onboard equipment.

The EMH is unusual in that he has his own separate computer hardware, but it's still very much non-portable, integrated into the ship.
The Mobile Emitter is the product of hundreds of years of refinement and doesn't count for our purposes.

Data however is a human-level intelligence AI housed in a human-sized brain (as evidenced by how he can continue to think and talk when his head is severed in at least one or two episodes).
Practically unique in the series for that alone!

Design-Type

Apart from the hardware, the EMH and similar AIs are explicitly modelled on existing people, both physically and personality-wise.
The Soong Androids are not. They're an effort to produce AI that grows into its personality from a low baseline (if anything), rather than being a highly sophisticated simulation of a person that has enough intellect to grow from there.

Different approaches, with different limitations and requirements.

The major difference is potential capability.

Holographic AIs are hardware limited. You don't want them to interact with something, you don't put any emitters around and isolate them from networks. You could make a power-mad AI and leave them in a box with a speaker, and they could rant away all they wanted and perhaps try and annoy you to death, but that's about it as long as you aren't an idiot and allow them voice access to another computer. As demonstrated in various episodes, you can alter their psychology, delete specific memories, fool around with skill sets by allowing them access or not to subroutines and information, basically treat them like computer programs. One starts getting big for its britches, turn off the computer and reboot them and they're back to their pleasant personality before they went insane.

The Soong-type androids however, are something different. By design, they've got at least the same physical capabilities as humans or others, usually more in terms of physical and mental abilities. They're not as easy contain, and, as shown in various episodes, it's not that easy to simply mentally alter them; despite Lore being a threat, Soong wasn't able to make him moral or erase the memory of what he'd done. One of the major issues in the episode Clues was that Data couldn't simply have the memory of the last 24 hours erased like everyone else, and that powering down and rebooting him didn't reset him.

So given an AI that is physically limited in its capabilities and can be easily controlled and prevented from becoming dangerous (despite the fact they keep making that stupid mistake, see M-5, Control, Moriarty, etc), versus one that by design is not limited in the same way, there's an obvious reason why people would be blasé about holographic AIs versus the androids. If the AI butler in the holodeck plans to kill you, it's trivial to deal with. If your android butler wants to kill you, you're screwed.