Bulgaria is automatically more powerful, and quite likely to have a stronger navy. This might not create a big rivalry between Romania and Bulgaria, since the region is historically Bulgarian land, however, the Romanians would want access to the sea, so it could. Assuming Bulgaria has a larger navy, it makes it easier for it to split off from turkey when the time comes, and means that the Balkan League has another member with a significant navy (OTL Greece carried them at sea). The greater control over the black sea means the possibility of naval attacks in northern Anatolia, so basically, the Balkan League does better/the war ends quicker.
I have a feeling that the Romanians would try to take Dobruja in the second Balkan war, prompting an earlier entry. TTL the Bulgars might fare a bit better in the eastern theatre of the second Balkan war, but would still lose land to Greece and make no gains in Serbia. They would likely end up losing at least part of Dobruja to Romania, and the border in Thrace would still be moved.
ends up looking something like this:
Northern (OTL) Bulgaria has a larger Muslim population than Dobruja, and the Turks there are generally on good terms with the Bulgarian government. I think they'd be able to deal with it just fine.
Southern Dobruja would likely be seen as "naturally" Bulgarian(due to history and the majority Bulgarian population), and they wouldn't lose it post-WWI.
The larger Bulgarian navy wouldn't be too useful in WWI.