Here's a fun set of exercises that I've been playing around with on my practice pad. They consist of two paradiddle-diddles with a paradiddle at the end. The sticking stays the same in each exercise, but the accent pattern varies.
In 1-3 the accents are on the 1st, 2nd or 1st and 2nd notes of the paradiddle-diddle and paradiddle. A-D then combine those accent patterns to come up with more interesting phrases.
First off, just get comfortable with the sticking (don't worry about the accents) and once you have a feel for it add the accents back in and focus on the dynamics.
The accents should be loud and (unsurprisingly) the unaccented strokes should be quiet — The greater the contrast between your loud and quiet strokes, the better it'll sound.
The next step is to make these ideas your own. Here are some suggestions:
Try combining the exercises to make longer (and more interesting!) phrases.
Swap the order of the paradiddle-diddles and paradiddle.
Accent the sticking in a different way. There are so many options here. If you want a challenge, try accenting the first or second note of the RR or LL.
Play them around the kit. Accents on the toms, unaccented notes on the snare.
Try to incorporate them into your playing. They can easily be adapted to make interesting fills, solos or even grooves.
PDF download: Paradiddle-diddle vs Paradiddle