Actually, India have a long way to go before they can be compared to England in Tests. And, also, India are just going through a bad patch in ODIs. Therefore, on the other hand, England also have a long way to go before they can be compared to India in ODIs.
Let's not forget, India still have to prove themselves in foreign conditions in Test matches, they have been throughout history very poor tourists. So it's not like India are really that great, in fact even at home a second string England attack managed to tie the series with them. England have also proven themselves in South Africa, where not many teams do well. On the contrary, in ODIs, India are just passing through a lean phase. Unlike England, who are very much poor and lack basic talent when it comes to ODIs.
In conclusion, no India are not becoming like England because India still have a lot to prove before they can be compared to relatively good Test teams like England and as far as ODIs are concerned... No India don't fail miserably in ODI, they are just terribly out of form and the same wouldn't have been said 7-8 months ago.