I don't think that "sea power" would have been the dominant issue had the Germans been able to secure "air superiority". Similarly the Brit Army was heavy equipment poor post Dunkirk and would have had a hard time opposing a mechanized force (which some but by no means much of the German Army was then). I'd put my money on air power.
The Channel is a very narrow corridor which would handicap freedom of action for any naval force without local air superiority. German air superiority and a localized flooding of the operational region with submarines would have greatly impeded British naval forces.
On the other hand, Germany was very handicapped in the quality and quantity of landing craft and other sea transport capabilities needed in order to secure a beachhead and to sustain it indefinitely. With the British capable of achieving local air superiority there would have been no chance of success.
I wonder how far the Americans could have gone vis a vis Europe without Britain as a base for building up their force? Africa? For Operation Torch the Western Task Force of 35,000 troops including two infantry divisions and a part of an armoured division did sail directly from the US.
Without the UK in play much of the German Atlantic Wall defence structure could have been greatly reduced. By D-Day, the Atlantic Wall consisted of some 1.8 million men in 58 divisions with 3,300 guns and 1,300 tanks which could well have been used elsewhere.
Would the US have bothered with Germany at all if Britain had fallen? Very debatable.
I tend to agree with you on the Pacific. The Japanese knew that the US was hemming them in and limiting their access to natural resources that they needed. There were other options for them but as of Dec 7th, 1941 the US wasn't involved in Europe anyway (except in minor ways). I think with the loss of Britain, the Japanese would have been even more inspired to act aggressively considering that British possessions in that part of the world would have been even more vulnerable to takeover and that the contemplated loss of much of the US fleet in Hawaii would open up the seas to them completely was even more valid.