I never saw the show on Broadway, or in it's Denver run, or even it's latest tour, but I did see a local production which used the new format and I'm also very familiar with the OBCR.
Personally, I really liked most of the additional songs. They felt really unnecessary, and yes, some songs felt out of place, but there were some really nice ones in there!
I loved Sweet Child and it's reprise, I thought Her Voice was stunning, and If Only and it's many reprises and pre-reprises nearly brought me to tears by the end!
Now, the show was very painfully flawed and possibly the worst Disney screen-to-stage adaptation made so far. But that being said, there were some very good moments added, I thought. I just tried not to compare it to the film, and that helped a lot.
I can't really defend The Contest... but I will say, it did get a chuckle out of me. I did like how sweet the scene got towards the end before Ursula popped in. Also, during the scene at the end-ish when Ursula confesses to killing Ariels mother, the underscoring, while simple, did give me chills. Also, I love the reprise of Poor Unfortunate Souls.
I also really liked that they at least attempted to make Prince Eric more interesting.
I enjoyed the show much more than I thought I would. I know it wasn't well done, and it's dialogue and pacing was painfully bad a lot of the time, but I found charm in it.