You have a tiny change in gearing, which you can calculate by measuring the outer diameter and plugging it into a calculator like this one -- the larger size will give you higher gearing (i.e. for a given cadence (# of times you turn the pedal per time unit), you'll go faster). You can use this calculator to calculate the difference in speed for a given cadence and gear combination and compare across the two tire sizes.
As for width, its a bit narrow for the rim, but you can technically get any 700c tire onto any rim. Running a too narrow tire though increases risks of pinch flats/rim damage. Running too wide a tire increases sidewall/rim failure risk, plus sloppy handling. That being said, this isn't an egregious violation, so you're probably fine. Make sure your frame+fork clear this bigger tire size with an appropriate margin (depending on your preferences, this could be 3-5 mm as the minimum distance between the tire and the fork/frame).
As for tube sizes, you can violate the marked sizes by a few sizes. A tube is a balloon -- you're just inflating the balloon a bit more than it was designed for, so it will be fine. If you go a lot more (say a 23c tube in a 5 inch tire), you'll have problems. You can probably put your existing tube in the new tire and have it work fine.
As for tire pressure, the thing written on the sidewall is an ad-hoc number (drawn jointly by the legal and marketing departments). Most people should be running a significantly lower pressure than what is marked for a properly inflated tire -- the tire deflects a bit, but has good rolling resistance and hazard+shock absorption properties. Even if you're ~250 lbs with bike+yourself, you're not going to need 100 PSI on a 700x28. And if you're getting near the max pressure, chances are you need to move to a bigger tire size anyway.
Finally, the real answer: If you swap between 25 and 28 and set the tire pressures appropriately, most people (esp. non-racers) will not notice a difference in performance. The 28 will be a bit more comfortable since its running at a lower pressure. For a 50 x 11, at 80 rpm, you're looking at 28.5 (25c) vs 28.9 mph (28c). For a 50 x 23 at 80 rpm, you're looking at 13.6 mph vs 13.8 mph. In any case, unless you're spinning out on top gear, you're not going to notice.