the number of variables here makes any 'this does that' type of analysis pretty redundant. If all other factors remain the same then a wider lay will be, as Pete says, harder to play, and also louder and 'bigger' in tone.
Also, a wider tip opening tends to make for easier and better pitch-bending. However, if it's more volume and a better tone you're after, you can get it by going up a reed strength. I've recently moved from Rico Jazz Select 2 Hard to 3 Soft, which is not a great leap in strength, and takes very little additional puff, but the difference in tone and volume is noticeable.
Warning: Large increases in tip opening might cause severe exhaustion of the lips, stretching of the patience and reversion to previous mouthpieces.
Compensatory decreases in reed strength may cause frustration while attempting to control the tone of the new and unruly beast on the end of your saxophone.
Good luck and if you can, make sure you try before you buy with a few different reed combinations. I have owned a few mouthpieces which were a little reed-fussy-
Tengu is dead right there, it's probably advisable to go for a fairly small increase in tip opening rather than going for a big leap. I 'accidentally' bought a Beechler piece for my alto, which has a substantially bigger tip than my other mpc's, and I very rarely use it as it tires my lips very quickly. Nice tone, though.
Cheers, Bob
Similar threads... or are they? Maybe not but they could be worth reading anyway 😀