しかし details

Examples

however; but — sets the following sentence against the previous one

何度なんども練習れんしゅうした。しかし、本番ほんばんでは手てが震ふるえた。

nando mo renshuu shita. shikashi, honban de wa te ga furueta.

I practiced over and over. Yet on the day itself my hands shook. neutral

売上うりあげは昨年さくねんを上回うわまわりました。しかし、利益りえきは横よこばいのままです。

uriage wa sakunen o uwamawarimashita. shikashi, rieki wa yokobai no mama desu.

Sales exceeded last year's figures. However, profits have stayed flat. neutral

本ほん研究けんきゅうの結果けっかは仮説かせつを支持しじしている。しかし、標本数ひょうほんすうが十分じゅうぶんであるとは言いい難がたい。

honkenkyuu no kekka wa kasetsu o shiji shite iru. shikashi, hyouhonsuu ga juubun de aru to wa iigatai.

The results of this study support the hypothesis. However, the sample size can hardly be called sufficient. formal

が
Both are the formal-register "but", split by sentence boundary — が normally joins the two halves inside one sentence (検討けんとうしましたが、見送みおくります), while しかし needs the first half already closed with a full stop; sentence-initial が exists but is a terse literary flourish, not the everyday choice.
ところが
ところが commits to surprise — what follows must defeat an expectation the reader already holds — while しかし only sets two propositions against each other and can mark a flat, unsurprising contrast (売上うりあげは伸のびた。しかし、利益りえきは横よこばいだ), which is why balanced argumentative prose takes しかし and a narrative twist takes ところが.
でも
Pure register — でも is the conversational default and is at home in chat and casual mail, while しかし belongs to writing and prepared speech; でも in an essay reads slack, and しかし in ordinary chat reads like a lecture.