Caps do sound different from each other (at least to me), but whether you'll like a new one depends on your ears and the circuit it's in. So no universal recommendations are possible. The Jantzen Z-caps you mention are good, quality caps and very affordable. I say you try them and see if they sound better to you than the stock caps. If they do, great. If they sound the same, then you'll know that rolling caps isn't for you (and no judgment there; plenty of people whose ears I respect don't hear differences between caps).
If you do hear a difference but you don't like it, you can put the stock caps back in and be thankful for conducting an inexpensive experiment Or you can go down the rabbit hole like many of us. You can try something like a Mundorf Supreme (or Silver Supreme) if you want a zippier or more highlighted treble. If you want a more mellow sound, try some paper-in-oil caps. Miflex caps, made in Poland, are very nice, pricey ($35 each for 0.1uF), but a relative PIO bargain compared to Dueland, AudioNote, or Jupiter.
