Full investment in Forex with no leverage vs partial investment with high leverage

Assume two investors with $100,000 each, willing to invest them in Forex as scalp.

Investor (a)

• Funds a brokerage account with the full $100,000
• each trade is executed with the full $100,000.
• trades with no leverage
• set a stop-loss to 1% of the investment ($1,000) per trade

Investor (b)

• Keeps $99,000 safe in his/her bank account.
• Funds the brokerage account with only $1,000
• each trade is executed with the full $1,000
• trades with 1:100 leverage (just trade broker leverage, not banking)
• doesn’t place any stop loss

Both investors execute the same trades.

Are these two strategies effectively the same in terms of risk and expected financial outcome? Will both get to the same final outcome?
Is option (b) safer and therefore recommended to maximize benefit while minimizing risk or does it have any flaw in the logic?