It was not technically Obi-Wan's choice, it was Yodas (as the leader of the Jedi and as Obi-Wan's superior).
Obi-Wan did not object though.
In the movie (which is considered absolute canon or G-cannon):
187 EXT. CORUSCANT -PADME'S APARTMENT-VERANDA-AFTERNOON
OBI-WAN: He has become a very great threat. As PADME moves to sit down, she reveals her pregnancy.
226 INT. POLIS MASSA-MEDICAL CENTER-NIGHT
OBI-WAN: She's dying?
MEDICAL DROID: We don't know why. She has lost the will to live. We need to operate quickly if we are to save the babies.
BAIL ORGANA: Babies??!!
MEDICAL DROID: She's carrying twins.
YODA: Save them, we must. They are our last hope.
233 INT. ALDERAAN CRUISER-CONFERENCE ROOM BAIL ORGANA, YODA, and OBI-WAN sit around a conference table.
YODA: Pregnant, she must still appear. Hidden, safe, the children must be kept.
OBI-WAN: We must take them somewhere the Sith will not sense their presence.
YODA: Split up, they should be.
BAIL ORGANA: My wife and I will take the girl. We've always talked of adopting a baby girl. She will be loved with us.
OBI-WAN: And what of the boy?
YODA: To Tatooine. To his family, send him.
OBI-WAN: I will take the child and watch over him. Master Yoda, do you think Anakin's twins will be able to defeat Darth Sidious?
YODA: Strong the Force runs, in the Skywalker line. Hope, we can . . . Done, it is. Until the time is right, disappear we will.
This leaves us a couple of things to consider:
- They took steps to make it look like Padme died still pregnant. This would prevent anyone for looking for the child/children.
- It is very likely that no one new that Padme was pregnant with twins since she had been keeping her pregnancy a secret (except possibly her medical droid).
- They did not deliberate over the children. One idea was presented and accepted for both babies.
- The goal was to prevent the Sith from detecting them (so where ever they were would need to be fairly well populated, preferably with naturally high amount of force presence).
- Neither child was all that well hidden (Luke went back to Anakin's step siblings on the plant where Anakin spent the first 9 years of his life. Also, they did not bother to change Luke's last name or try to replace his father so he was no longer an orphan).
- The Organa's already had a cover story (they had been talking about adopting a baby girl) which would reduce suspicion concerning the origin of the child.
- The Jedi were very limited on allies and resources. They had to take what they could get.
- They were in the middle of a war which had caused many casualties. As such there were probably many orphans which could be used to obscure the origins of Luke and Leia.
While the power and influence she would have being raised as an Organa would be beneficial, it is fairly clear that it was not a reason for their decision.
That being said, it is also important to remember that Leia was Princess Organa first, and revealed to be Luke's twin later. As a result, the events which got her adopted is a patch to the problem introduced in Episode 6.