Is the fundamental data provided by financial websites generally comparable across companies?

Nominal amounts like net profit typically aren't comparable between companies of different size. What's more comparable within an industry are financial ratios like return on assets, net profit margin, etc.

Note that even then, one metric cannot be used alone to determine if one company is a better investment than the other. Many metrics must be considered since companies can have different management and financing philosophes (e.g. debt vs equity) that can some ratios in a way that makes the company look better but makes other ratios look worse.

Would the answer change if PepsiCo and Coca-Cola were (hypothetically) incorporated/headquartered/listed in different countries (e.g. PepsiCo in country X, Coca-Cola in country Y)?

Sure - differences in currencies, laws, regulations, markets, etc. can make large differences in how companies operate, which can be reflected in their financials.