Its like cross breeding in most other areas. If you take 2 things with differing traits but compatible reproductive systems, what you end up with is a mix of various components of the 2 parents, but to varying degrees. Some traits can be dominant while others are easily suppressed. Often times it takes multiple generations of cross pollinating to get specific attributes like size, color, sugar content, etc. up to where you want them. Even Self fertility and self pollination are genetic traits that may or may not survive a crossing.
Also, regardless of what species you pollinate with, you'll always get a fruit that matches the flowering plants species. Its the seeds that get the new genetic code. You don't change the womb with new pollen.
Also Ric, the thing with cross pollinating creating bigger fruit is not on a genetic level, but on a abundant fertility level. The the only way I can explain it is that using another species' pollen actually makes the flower you put it on generate a bigger fruit, which I think is a result of more successful pollen acceptance, which generates more seeds per individual fruit. Like twins in a single womb. I don't know if this is fact or speculation, and Ive never experimented with this as I normally use a single species type of pollen for all my plants (as long as its available). It wont cause the seeds to generate plants that produce bigger fruit, unless that is one of the specific genetic markers that gets handed down from the chromosome paring.