Yes and no. Republicans inherited the economic ideology of the Whig Party and tended to attract many of the same demographics in the North. Most Northern Whigs also became Northern Republicans, and the party tended to be dominated by former Whigs like Lincoln and Seward. Lincoln was a massive supporter of Henry Clay, to Whigs what Andrew Jackson is/was to Democrats. Lincoln declared in one of his first political speeches that he supported Clay and "My politics are short and sweet, like an old woman's dance. I am in favor of a national bank. I am in favor of the internal improvements system and a high protective tariff." Lincoln's statement contains the three main platforms of Henry Clay's American system. Lincoln would later call Clay his "beau ideal of a statesman". The most eloquent statements on the part of Lincoln regarding Clay were during the eulogy he gave at the Illinois State house in Springfield. A full record of the eulogy can be found here and it is well worth reading. In particular Lincoln stated that

"Throughout that long period, he has constantly been the most loved, and most implicitly followed by friends, and the most dreaded by opponents, of all living American politicians. In all the great questions which have agitated the country, and particularly in those great and fearful crises, the Missouri question -- the Nullification question, and the late slavery question, as connected with the newly acquired territory, involving and endangering the stability of the Union, his has been the leading and most conspicuous part"

Interestingly Lincoln doesn't criticize Clay's stance on slavery as abolitionists were more prone to do. Rather he lauds Clay's efforts in the ACS stating

"Having been led to allude to domestic slavery so frequently already, I am unwilling to close without referring more particularly to Mr. Clay's views and conduct in regard to it. He ever was on principle and in feeling, opposed to slavery. The very earliest, and one of the latest public efforts of his life, separated by a period of more than fifty years, were both made in favor of gradual emancipation of the slaves in Kentucky. He did not perceive, that on a question of human right, the negroes were to be excepted from the human race. And yet Mr. Clay was the owner of slaves. Cast into life where slavery was already widely spread and deeply seated, he did not perceive, as I think no wise man has perceived, how it could be at once eradicated, without producing a greater evil, even to the cause of human liberty itself. His feeling and his judgment, therefore, ever led him to oppose both extremes of opinion on the subject. Those who would shiver into fragments the Union of these States; tear to tatters its now venerated constitution; and even burn the last copy of the Bible, rather than slavery should continue a single hour, together with all their more halting sympathisers, have received, and are receiving their just execration; and the name, and opinions, and influence of Mr. Clay, are fully, and, as I trust, effectually and enduringly, arrayed against them."

Finally Clay's great speech at the 1850 compromise was one of the four references Lincoln used in his first inaugural. I think it is therefor safe to say that Lincoln was a big fan of Clay, and the Whig party itself.

The difference lies primarily with slavery. While Whigs were arguably better on slavery than Democrats* ( and here I define better as being less supportive of slavery) they were not explicitly a party founded on opposing slavery. This isn't to say that they didn't have those who were opposed to slavery, John Quincy Adams and the Massachusetts conscience Whigs were particularly noted for their attacks on slavery and Whigs were much more likely to oppose measures like the gag rule. Other similarities included an opposition to expand the United States, namely in Indian Removal, Texas annexation and combating attempts to take Mexican Land during the Mexican-American war. Whigs ultimately had to serve the needs of both Northern and Southern wings of the party, their inability to do so lead them to fracture and then break by the early to mid 1850's. Many of those in the Upper South continued to hold onto Whig ideology, past the breakup of the Whig party. These men even went so far as to ask the Republicans to drop their anti-slavery platform so they could have once again a national party to belong too. Lincoln himself actually enjoyed a healthy amount of support in the border South, usually from former Whigs. For instance he won 10% of Missouri's vote, and one of the first Republican vice-presidential prospects was none other than Henry Clay's cousin Cassius Clay. Even more importantly Lincoln likely wouldn't have won the Republican nomination without the support of the Republican delegates from the South.

• Howe gives the best argument that the Whigs were "better" on slavery in What Hath God Wrought, William Freehling gives an alternative perspective in Secessionists at Bay emphasizing that it was Whigs from the deep South who often proposed the harshest measures in defense of slavery. Both books are well worth reading as is Howe's book The Political Culture of the American Whigs

Edit: I may have misinterpreted your question. By the mid 1850's there were a number of parties vying to replace the Whigs as the opposition party to the Democrats, in the sense that Republicans arose to be the main opposition to Democrats they absolutely replaced the Whigs.