I'm on Tecfidera. Yes, it can have some stomach upsets - for me it was and is mainly nausea, but a super weird type, as in I am a bit crampy and nauseated yet the thought and smell of food doesn't really make me want to hurl. Very odd. In any case it has subsided now that the first month is over, and they do have some pretty fine meds for nausea: Zofran is your FRIEND.
Gilenya seems to have more of a side-effect list than Tec, and more preliminary testing (eyes) and prelim monitoring(first dose has to be monitored by medical people for heart rate issues) to be done. Tec has less BUT can drive your white count down AND there has been at least one documented case of PML with it. Since close monitoring of blood counts should be able to head that risk off at the pass, I opted for the Tec. Other than the nausea and a tiny bit of flushing, I've not had terrible problems so far. (Getting ready to start month 3).
And as HVAC says, not all meds are equally effective for all presentations of MS. I'm older and presenting with classic motor symptoms right off the bat, my neuro pretty much blew by copaxone as an option, said it was more appropriate for vision and sensory issues. He went straight for the big guns with me. We shall see. I've had 2 new lesions between Oct and Dec (dec being when I started the Tec) and one flu-induced relapse (new lesion) since I started the Tec, (only 21-25 days into the first month) so we still don't have a good feel for how well it will work for me. But I'm still hopeful.
If you don't have heart condition either. They can both have side effects. If you have been offered the injectable there is a reason. The injectable have less side effects. They are good for early MS. The pills were designed for people with more disabilty from MS usually people who have been on the CRABs and none have worked or they stopped working.
Both Gilenya and Tecfidera for example can cause digestive issues. I have never been on either only Copaxone.
Also these two drugs have not been around long enough to know what there long term effects might be.
I understand not wanting to do shots.
Alex