Stifel resumed coverage of Home Depot and Lowe's today, putting a "buy" rating on each stock.

Behind Stifel's call is the firm's belief that home improvement spending is on the rise.

"It is our view that spending on the home is currently accelerating after a 6-8 year period of under-spend due to the collapse of the housing market. Home prices are accelerating, which improves consumers' balance sheet and fosters confidence in spending on the home...Our coverage of many of the vendors selling into Home Depot and Lowe's indicates business is improving currently," Stifel's John Baugh wrote.

With a $157 price target on Home Depot -- a 15% upside -- and a $100 target on Lowe's -- a 22% upside -- the firm sees room for the stocks to run.

On the "Halftime Report" today the desk debated the call, and whether or not the home improvers are heading higher.

Stephanie Link owns Lowe's and is sticking with her trade.

"I prefer Lowe's over Home Depot maily because they [Lowe's] are in the process of restructuring and reorganizing...there's more they can get out of the margins story, and there's more they can get out of the pro-side of the business because they don't have as big of a presence," she argued.

Stifel points out that Home Depot is "the sixth largest internet retailer in the U.S.," a fact that Pete Najarian thinks investors overlook.

"The I.T. spend at Home Depot is something they've really been rewarded by," Najarian said on the "Halftime Report." Coupled with the company's "strong" management team, Home Depot is Najarian's top pick in the sector.

Like Stephanie, Josh Brown prefers Lowe's to Home Depot since he believes Lowe's is "under-owned relative to Home Depot. This [Lowe's] could be a triple-digit name over the next couple of years."

Brown does note, however, that since the home-improver space is growing, there is room for both companies to prosper.

Trader disclosure: On August 2, 2016 the following stocks and commodities mentioned or intended to be mentioned on CNBC's "Halftime Report" were owned by the "Halftime Report" traders:

Pete Najarian: Long Stock: AAPL, BAC, BMY, CSCO,DIS, DISCA, GE, KMI.A, KMI, KO, LUX, MRK, PEP, PFE, VIAB. Long Calls: AAL, ABT, AKS, ANF, BSX, BZH, CHK, CIT, CNX, COP, DAL, DVN, FB, GILD, HALO, HOG, INTC,KGC, LLY, MCD, MPEL, MRO, MT, NEM, NGD, P, PG, PSX, SCHW, SLV, SLW, TMUS, VLO,XLE, YELP. Long Puts: CS, EEM, MBLY, NLY

Josh Brown: Long AAPL, AMGN, CORE, DE, DNKN, GE, SAM, SHAK, TWTR, XLE

Stephanie Link: Long AAPL, AGN, AIG, AMZN, APC,AVGO, BAC, C, CAG, CAT, CB, CSCO, CVX, DOW, EBAY, EL, ESRX, FB, GOOG, GOOGL,GS, HON, INTC, JPM, LEA, LLY, LOW, LPX, LRCX, MDLZ, MGM, MSFT, PG, PM, PPG, RTN, SLB, STI, SWK, TGT, UNH, UPS, URI, V, WBA, WBC, WFC, WHR, YUM

Joe Terranova: Long VRTS