We had the exact same question here last week but I can't find it now to link for you. But basically the answer is no difference unless the indoor one is better..

Once color break happens the fruit is sealed off from the plant by a membrane that only water can permeate. So in the case of heavy rain for example the ones ripened indoors actually taste better. Plus they won't suffer from sun scorch or bugs or hail or squirrels etc.

Dave

E...this was discussed thoroughly on the other tomato forum. Dr. Carolyn Male who is a renowned expert and author on tomatoes was clear as to her thoughts. Paraphrased: tomatoes that remain attached to the vine still are capable of importing nutrients and water. She did not commit as to the "best" time to harvest. For most of us...if the threat of critters or bad weather is present, it is best to pick (after color). For most...the loss of taste is insignificant...if at all.

I have come to agree with Dave, fully.
Ripening can take place within a fruit, separated from vine, tree etc.
It happens all the time that certain fruits even OVER ripen after harvest. Unless they are refrigerated to slow down that process. I always buy peaches pears .. that are hard and not quite ripe. After a few days they become nice and juicy.
It is the same concept with tomato. Plus, picking them early offer added advantages.. for example you take the first bite before the squirrel does. lol

Thanks for your responses. I know it was a question that probably had been answered before, but I don't regularly follow this forum.

For what it's worth we've had lousy weather here in Western PA. for tomato growing this year, but I have a pretty good harvest from the 4 Big Boys and 4 Better Boys I put in. The started ripening around the 10th of this month.